arXiv research

In this note, we study the ultimate ruin probabilities of a real-valued L{é}vy process X with light-tailed negative jumps. It is well-known that, for such L{é}vy processes, the probability of ruin decreases as an exponential function with a rate given by the root of the Laplace exponent, when the initial value goes to …

This paper presents generalized momentum mappings for covariant Hamiltonian field theories. The new momentum mappings arise from a generalization of symplectic geometry to $L_VY$, the bundle of vertically adapted linear frames over the bundle of field configurations $Y$. Specifically, the generalized field momentum obs…

In this paper, we provide a representation theorem for dynamic capital allocation under It{ô}-L{é}vy model. We consider the representation of dynamic risk measures defined under Backward Stochastic Differential Equations (BSDE) with generators that grow quadratic-exponentially in the control variables. Dynamic capital …

This article is devoted to the maximisation of HARA utilities of L{é}vy switching process on finite time interval via dual method. We give the description of all f-divergence minimal martingale measures in initially enlarged filtration, the expression of their Radon-Nikodym densities involving Hellinger and Kulback-Lei…

In this paper, we study the ruin problem with investment in a general framework where the business part X is a L{é}vy process and the return on investment R is a semimartingale. We obtain upper bounds on the finite and infinite time ruin probabilities that decrease as a power function when the initial capital increases…

Let $M$ be a manifold, $V$ be a vector field on $M$, and $B$ be a Banach space. For any fixed function $f:M\rightarrow B$ and any fixed complex number $λ$, we study Hyers-Ulam stability of the global differential equation $Vy=λy+f$.

Modeling financial markets with a novel order flow model.

The Wiener-Hopf factorization is obtained in closed form for a phase type approximation to the CGMY Lévy process. This allows, for the approximation, exact computation of first passage times to barrier levels via Laplace transform inversion. Calibration of the CGMY model to market option prices defines the risk neutral…

We introduce a class of interest rate models, called the $α$-CIR model, which gives a natural extension of the standard CIR model by adopting the $α$-stable L{é}vy process and preserving the branching property. This model allows to describe in a unified and parsimonious way several recent observations on the sovereign …

We prove that a compact stratied space satises the Riemannian curvature-dimension condition RCD(K, N) if and only if its Ricci tensor is bounded below by K $\in$ R on the regular set, the cone angle along the stratum of codimension two is smaller than or equal to 2$π$ and its dimension is at most equal to N. This gives…

Many recent papers address reading comprehension, where examples consist of (question, passage, answer) tuples. Presumably, a model must combine information from both questions and passages to predict corresponding answers. However, despite intense interest in the topic, with hundreds of published papers vying for lead…

Constructs supermartingale couplings with full marginals constraints.

The distribution of trade sizes and trading volumes are investigated based on the limit order book data of 22 liquid Chinese stocks listed on the Shenzhen Stock Exchange in the whole year 2003. We observe that the size distribution of trades for individual stocks exhibits jumps, which is caused by the number preference…

We provide an empirical investigation aimed at uncovering the statistical properties of intricate stock trading networks based on the order flow data of a highly liquid stock (Shenzhen Development Bank) listed on Shenzhen Stock Exchange during the whole year of 2003. By reconstructing the limit order book, we can extra…

Paper introduces kernel deformed exponential families for sparse continuous attention.

Introduces a new theoretical framework for exponential smoothing.

New linear flows using exponential of linear transformations improve generative models.

Incorporates matrix exponential into generative flows for improved performance.

Study the exponential map on surfaces using fluid dynamics.

Exponential family distributions are highly useful in machine learning since their calculation can be performed efficiently through natural parameters. The exponential family has recently been extended to the t-exponential family, which contains Student-t distributions as family members and thus allows us to handle noi…

Study on stability of harmonic maps with sub-Riemannian geometry.

New exponential map for Lie groups connects to sub-Riemannian geometry.

The study explores generalized divergences and exponential families with a focus on sufficient conditions and laws of large numbers.

The paper proves exponential mixing for hyperbolic manifolds, with applications to geodesic holonomy.

Generalizes moment-matching for exponential families with conditioning or hidden data.

Correspondence found between exponential families and affine Grassmannians.

Groups on CAT(0) cube complexes grow exponentially uniformly.

In a Markovian stochastic volatility model, we consider financial agents whose investment criteria are modelled by forward exponential performance processes. The problem of contingent claim indifference valuation is first addressed and a number of properties are proved and discussed. Special attention is given to the c…

We construct 2-dimensional CAT(-1) groups which contain free subgroups with arbitrary iterated exponential distortion, and with distortion higher than any iterated exponential.

New hyperbolic manifolds show exponential homology torsion growth.

Establishes exponential contraction in Wasserstein distance on manifolds and flows.

New insights into natural exponential families improve regret bounds for bandit problems.

Study on hedging with delayed strategies for exponential utility maximization.

Proves properties of sub-Riemannian exponential map, showing it's not injective.

Exponential smoothers are a simple and memory efficient way to compute running averages of time series. Here we define and describe practical properties of exponential smoothers for signals observed at constant and variable intervals.

Thompson Sampling has been demonstrated in many complex bandit models, however the theoretical guarantees available for the parametric multi-armed bandit are still limited to the Bernoulli case. Here we extend them by proving asymptotic optimality of the algorithm using the Jeffreys prior for 1-dimensional exponential …

A new method for efficiently computing derivatives of skew-symmetric matrix exponentials.

We give several sufficient conditions for uniform exponential growth in the setting of virtually torsion-free hierarchically hyperbolic groups. For example, any hierarchically hyperbolic group that is also acylindrically hyperbolic has uniform exponential growth. In addition, we provide a quasi-isometric characterizati…

Exponential distribution is ubiquitous in the framework of multi-agent systems. An alternative approach with an economic motivation to derive the exponential distribution in the framework of iterations in the space of distributions is disclosed.

Proves new concentration inequalities for sub-gaussian and sub-exponential variables.

A new machine learning model uses matrix exponentials for universal approximation.

Constructing exponential families from statistical manifolds.

New Thompson sampling algorithm reduces regret for exponential family bandits.

Defines formal exponentials for graded manifolds and linearizes QP-manifolds.

Extends online learning to metric spaces using exponential weights.

Revisits stochastic collocation with exponential splines for option pricing.

A random walk $w_n$ on a separable, geodesic hyperbolic metric space $X$ converges to the boundary $\partial X$ with probability one when the step distribution supports two independent loxodromics. In particular, the random walk makes positive linear progress. Progress is known to be linear with exponential decay when …

We study the probability distribution of stock returns at mesoscopic time lags (return horizons) ranging from about an hour to about a month. While at shorter microscopic time lags the distribution has power-law tails, for mesoscopic times the bulk of the distribution (more than 99% of the probability) follows an expon…